Question

A researcher wants to estimate the proportion of manufacturing companies that use the six sigma method. For this purpose, she takes a random sample of 50 manufacturing companies and finds out that 28 of them employ this method. The 95% confidence interval for the proportion of manufacturing companies that use six sigma is ______.

Answer 1

Answer:  (0.392, 0.668)

Step-by-step explanation:

Given : Sample size : n= 50

The proportion of successes : $p=\dfrac{28}{50}=0.56$

Significance level : $\alpha: 1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

The confidence interval for population proportion is given by :-

$p\pm\ z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}\\\\=0.53\pm(1.96)\sqrt{\dfrac{0.53(1-0.53)}{50}}\\\\\approx0.53\pm0.138\\\\=(0.392,\ 0.668)$

Hence, the 95% confidence interval for the proportion of manufacturing companies that use six sigma is (0.392, 0.668).